

A287688


Triangle read by rows: T(j,k) is the number of distinct edge segment pairs in a j X k rectangular grid.


2



2, 6, 7, 10, 15, 13, 15, 21, 28, 22, 21, 28, 36, 45, 32, 28, 36, 45, 55, 66, 45, 36, 45, 55, 66, 78, 91, 59, 45, 55, 66, 78, 91, 105, 120, 76, 55, 66, 78, 91, 105, 120, 136, 153, 94, 66, 78, 91, 105, 120, 136, 153, 171, 190, 115, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 137
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OFFSET

1,1


COMMENTS

This gives the number of pairs of edge segments that are distinct with respect to rotation and mirror images. Sequence is arranged so that j <= k (since 2 X 3 and 3 X 2 are equivalent grids), first by increasing j, then by increasing k: a(1) = 1 X 1 = 2, a(2) = 1 X 2 = 6, a(3) = 2 X 2 = 7, a(4) = 1 X 3 = 10.
Here j = A002260(n), k = A002024(n), and n = A000217(k1) + j.
Where j != k, a(n) = A000217(j + k).
Where j = k, a(n) is approximately A236312(j2); a(n) >= A236312(j2).


LINKS

Doug Bell, Table of n, a(n) for n = 1..11325, rows n = 1..150, flattened.


EXAMPLE

Triangle begins:
2;
6, 7;
10, 15, 13;
15, 21, 28, 22;
21, 28, 36, 45, 32;
28, 36, 45, 55, 66, 45;
36, 45, 55, 66, 78, 91, 59;
...
For n = 3, the a(3) = 7 pairs of edge segments for a 2 X 2 rectangular grid are:
+   + + * * + + *  + + *  + + *  + + *  + + *  + + *  +
  \    *         * 
  /      *     *   
+   + +   +, +   +, +   +, +  * +, + *  +, +   +, +   +.


CROSSREFS

Cf. A002260, A002024, A000217, A236312. Distinct edge segments A287618.
Sequence in context: A047552 A287453 A287449 * A221847 A283766 A047216
Adjacent sequences: A287685 A287686 A287687 * A287689 A287690 A287691


KEYWORD

nonn,tabl


AUTHOR

Doug Bell, May 29 2017


STATUS

approved



